Lecture 5

Resource Allocation Over Time

Byeong-Hak Choe

bchoe@geneseo.edu

SUNY Geneseo

September 21, 2026

💵 The Discount Rate

❓ Resource Allocation across Generations

How should a limited natural resource be divided across generations?
How can we compare benefits and costs that occur at different dates?
What happens to prices and consumption as a resource becomes scarce?

🗓️ Values at Different Dates

Costs and benefits often occur at different dates.

Expressing amounts in real dollars removes inflation. It does not make a future dollar equivalent to a current dollar.

A positive discount rate reflects the return available elsewhere and the weight placed on earlier consumption.

Discounting converts a future real amount into its present value.

🔁 Discounting Reverses Compounding

Let $PV$ be today’s amount and $X_t$ its value $t$ years later at a constant annual rate $r$.

\[ \begin{aligned} \text{Year 1:}\quad X_1&=\underbrace{PV}_{\text{principal}} + \underbrace{r\,PV}_{\text{interest}} =PV(1+r).\\ \text{Year 2:}\quad X_2&=\underbrace{X_1}_{\text{principal}} + \underbrace{rX_1}_{\text{interest}} =X_1(1+r) = PV(1+r)^2.\\ \text{Year 3:}\quad X_3&=\underbrace{X_2}_{\text{principal}} + \underbrace{rX_2}_{\text{interest}} =X_2(1+r) = PV(1+r)^3.\\ \end{aligned} \]

The pattern continues:

\[ \text{Year t:}\quad X_t=PV(1+r)^t\qquad\qquad\qquad\qquad\qquad\quad\; \].

🧮 Present Value

Let $X_t$ be an amount received in $t$ years and let $r$ be the annual discount rate.

\[ PV(X_t)=\frac{X_t}{(1+r)^t}. \]

Present value falls when the date moves farther into the future.

Present value also falls when the discount rate rises.

Use real future amounts with a real discount rate.

🔢 PV of $100 across Rates and Years

A heatmap shows the present value of 100 dollars at discount rates from 1 to 10 percent and horizons from zero to 100 years. Present value falls as the rate or time horizon increases. — Figure 1

🌎 A Long-Term Policy Example

Suppose a policy prevents $500 billion in climate damages 50 years from now.

Which present value uses a 2% rate, and which uses a 5% rate?

$185.8 billion
$43.6 billion

The future benefit is unchanged. The rate changes its present value and can change the policy decision.

🏙️ Quick Detour: Manhattan and Compounding

Suppose the often-cited $24 figure had instead been invested at an assumed annual return of 4.66% from 1626 to 2026.

Four hundred years of compounding gives

\[ FV_{2026}=\$24(1.0466)^{400}\approx\$1.96\text{ billion}. \]

Over 400 years, even a small change in the assumed return produces a very different future value.

This is a compounding illustration, not a historical appraisal of Manhattan land.

✌️ Quick Detour: The Rule of 72

The Rule of 72 estimates how long a value takes to double at a constant annual rate.

\[ \text{Years to double}\approx\frac{72}{r}, \]

where $r$ is written as a percentage rather than a decimal.

At 3% per year, doubling takes approximately 24 years.

The rule works best for moderate rates and provides intuition for compounding and discounting.

🧭 A Fixed Stock across Generations

🌍 Two Kinds of Resource Stock

This lecture focuses on nonrenewable resources, using neodymium as the main example.

Renewable resources regenerate through ecological processes.

Forests and fisheries can remain productive when harvest does not repeatedly exceed growth.
Renewable does not mean impossible to deplete.

Nonrenewable resources do not regenerate on a human time scale.

Oil, coal, and mineral deposits are examples.
One unit extracted today cannot also be used later.

🧲 Neodymium Model Setup

An educational illustration showing a mineral mine, neodymium-bearing ore, separated rare-earth oxide, and a permanent-magnet electric motor.

Resource: 250 model tons of recoverable neodymium in one known deposit
Use: permanent magnets in electric motors and some wind turbines
Market: magnet manufacturers’ WTP compared with marginal mining, separation, and processing cost
Time and stock: two periods, ten years apart, with one fixed stock and no discoveries
Benchmark: illustrative equations omit joint production, recycling, substitution, and environmental harm

📊 Neodymium Market Model

🧮 Current Demand and Supply

Demand:

\[ P_D=150-0.25Q. \]

Supply:

\[ P_S=50+0.25Q. \]

$Q$ is model tons of recoverable neodymium. $P$ is an illustrative price, not a market estimate.

Demand measures magnet manufacturers’ marginal willingness to pay. Supply measures marginal mining, separation, and processing cost.

⚖️ Static Neodymium-Market Equilibrium

Demand for recoverable neodymium slopes downward and supply slopes upward. They intersect at 200 model tons and 100 dollars per ton. — Figure 2

➖ Marginal Net Benefit

Marginal net benefit is marginal benefit minus marginal cost:

\[ MNB=P_D-P_S. \]

For this illustrative market,

\[ MNB=(150-0.25Q)-(50+0.25Q). \]

\[ MNB=100-0.5Q. \]

🔺 Total Net Benefit

Marginal net benefit falls from 100 to zero at 200 tons. The triangular area beneath the curve is 10,000 dollars. — Figure 3

🧾 Static Equilibrium

At $Q=200$,

\[ MNB=100-0.5(200)=0. \]

The area under MNB is total benefit minus total cost:

\[ TNB=\frac12(200)(100)=10{,}000. \]

A static equilibrium counts only present benefits and costs.

🕰️ Put Two Periods on One Clock

↔︎️ The Stock Constraint

Suppose the known deposit contains 250 model tons of recoverable neodymium.

\[ Q_1+Q_2=250. \]

The two periods have the same undiscounted marginal net benefit:

\[ MNB_1=100-0.5Q_1, \]

\[ MNB_2=100-0.5Q_2. \]

🪞 The Mirror Axis

Period 1 marginal net benefit slopes downward. Period 2 marginal net benefit is mirrored, and its discounted value is lower. — Figure 4

⏳ Discount Period 2

The periods are ten years apart.

\[ (1.0725)^{10}\approx2. \]

Therefore,

\[ PV[MNB_2]\approx\frac{MNB_2}{2}. \]

Discounting lowers every Period 2 marginal net benefit when measured in Period 1 dollars.

🎯 Dynamic Equilibrium

⚖️ Equal Values at the Margin

The efficient allocation satisfies both conditions:

\[ \begin{aligned} MNB_1 &= PV[MNB_2],\\ Q_1+Q_2 &= 250. \end{aligned} \]

For example, consider $Q_1=125$ and $Q_2=125$:

Here, $MNB_1=37.50$ while $PV[MNB_2]=18.75$.

Moving a small amount of neodymium from Period 2 to Period 1 would therefore raise discounted total net benefit.

Using these two conditions, solve for $Q_1$ and $Q_2$.

🟢 The Optimal Allocation

Period 1 marginal net benefit and discounted Period 2 marginal net benefit cross at 150 tons now and 100 tons later. Areas A and B are shaded. — Figure 5

🔻 Too Much Current Use Loses Welfare

Period 1 marginal net benefit and discounted Period 2 marginal net benefit cross at the efficient allocation. — Figure 6

A dashed line marks an allocation of 200 tons in Period 1 and 50 tons in Period 2. — Figure 7

The allocation of 200 tons now and 50 tons later creates a red welfare-loss triangle labeled Net loss B 2. — Figure 8

🧭 Dynamic Equilibrium

A dynamic equilibrium counts current and future benefits and costs.

At the crossing,

present-value marginal net benefit is equal across dates;
the full stock is allocated; and
no reallocation can increase discounted total net benefit.

💎 User Cost and Depletion Policy

🕳️ Current Use Has a Future Opportunity Cost

User cost is the future opportunity lost when one more unit is extracted now.

Period 2 would choose 200 tons in its static market.

If Period 1 uses more than 50 tons, fewer than 200 remain for Period 2.

From that point, another current ton displaces a desired future ton.

🧮 User Cost at the Efficient Quantity

From Period 1,

\[ MNB_1(150)=100-0.5(150)=25. \]

From Period 2,

\[ PV[MNB_2(100)]=\frac{100-0.5(100)}{2}=25. \]

The equilibrium user cost is $25 per ton.

🧾 Internalize User Cost in Period 1

Demand, extraction cost, social cost with user cost, and supply with a 25 dollar tax meet at the efficient Period 1 outcome of 150 tons and 112.50 dollars. — Figure 9

💵 The Resource Depletion Tax

A resource depletion tax charges for the future opportunity lost through current extraction.

At the target quantity,

\[ \tau=25. \]

The tax-adjusted supply curve is

\[ P_S=75+0.25Q_1. \]

Equating demand and tax-adjusted supply gives

\[ Q_1=150,\qquad P_1=112.50. \]

📦 The Remaining Stock Sets Period 2 Quantity

A vertical remaining-stock line at 100 tons meets Period 2 demand at a price of 125 dollars. — Figure 10

🇯🇴 Mineral Depletion and Future Income in Jordan

NASA satellite image of a phosphate mine in Jordan

Jordan mines phosphate and potash, two nonrenewable minerals used in fertilizer.
Extraction earns current income but gives up future income. User cost measures this tradeoff.
Using a 3% discount rate, one study estimated about $550 million in user costs during 2002–2010.
That estimate was about 20% of mining profits over the same period.
Reinvesting this portion of mineral income can build education, infrastructure, or renewable natural capital for future generations.

🧰 Policy Options for Conserving More for Later

A depletion tax adds the future opportunity cost to the current extraction decision.

An extraction limit directly caps how much may be mined now, but it requires measurement and enforcement.
A reserve keeps selected deposits underground for future use.
A public stockpile buys and stores processed neodymium material for later release, but storage is costly.

Discussion: To leave more neodymium for Period 2, would you use a tax, a limit, or a reserve? Why?

📈 Scarcity Rent and Hotelling

💰 Scarcity Rent When 50 Tons Remain

Demand and marginal extraction cost are shown with a remaining-stock limit of 50 tons. At 50 tons, the market price is 137 dollars and 50 cents, marginal extraction cost is 62 dollars and 50 cents, and the vertical difference is scarcity rent of 75 dollars per ton. — Figure 11

The stock limit fixes $Q_2=50$. The market price covers $62.50 of extraction cost plus $75 of scarcity rent, the value of using one unit of the limited stock.

🏦 A Forward-Looking Owner May Conserve

At the static split ($Q_1 = 200, Q_2 = 50$), the last ton sold now earns $0 of scarcity rent, but a ton saved for Period 2 earns $75, worth $37.50 today.

At the dynamic split ($Q_1 = 150, Q_2 = 100$), scarcity rent is $25 now and $50 later. With a ten-year discount factor of 2, $\$25=\$50/2$.

Discussion: When would a private owner’s allocation decision also coincide with the dynamic equilibrium?

Harris and Roach, printed p. 129. At the static split, $P_1=MC_1=\$100$ at 200 tons (static-equilibrium slide), so $R_1=\$0$; at 50 tons later (previous slide), $P_2-MC_2=137.50-62.50=\$75$, or $37.50 after dividing by the ten-year factor of 2. Owners shift tons to Period 2 until $R_1=R_2/2$, which gives 150 and 100 tons if the owners’ market rate is the model’s 7.25%. The result also needs many price-taking owners; a sole owner of the deposit would act as a monopolist and extract more slowly (about 128 tons now, 122 later). A higher market interest rate would move the private path toward Period 1 (see the next two slides). With an external damage of $d$ dollars per ton in both periods (for $d<\$37.50$, while the stock still binds), the efficient Period 1 quantity falls to $150-2d/3$, while owners who ignore it still choose 150: too much in Period 1 and too little in Period 2.

Harris and Roach note that markets are most likely to internalize user cost without policy when exhaustion is expected relatively soon.

The model also assumes one known stock, secure ownership, and no new discoveries, recycling, or technical change. A depletion tax is not needed when the current price already reflects user cost, but a separate policy may still be needed for external damages.

📉 Discount Rates Change the Allocation

A fan of discounted Period 2 marginal net benefit curves moves lower as the discount rate rises, shifting the efficient crossing toward more Period 1 use. — Figure 12

📋 Discount Rates Shift Use Earlier

Annual rateApprox. ten-year factor$Q_1$$Q_2$

Annual rate	Approx. ten-year factor	$Q_1$	$Q_2$
0%	1.0	125	125
2%	1.2	132	118
5%	1.6	143	107
7.5%	2.0	150	100
10%	2.6	158	92
15%	4.0	170	80
20%	6.2	179	71
30%	13.8	190	60

Higher rates give Period 2 less present weight and shift the efficient allocation toward Period 1.

📈 Hotelling’s Rule

Hotelling’s rule: in equilibrium, the net price of a nonrenewable resource rises at the market interest rate, $r$.

The net price is the scarcity rent on the last ton sold: $R_t=P_t-MC_t$, price minus marginal extraction cost in year $t$.

\[ R_{t+1}=(1+r)R_t \quad\Longleftrightarrow\quad \frac{R_{t+1}-R_t}{R_t}=r \]

Each year, the net price grows by the same percentage, $r$, as money in the bank.

🪙 One Ton, Two Choices

Today’s net price is $R_t=\$100$, and the market interest rate is 7%. What should an owner do with one ton?

Choice	Value next year
Extract now: invest the $100 net price at 7%	$100 × 1.07 = $107
Wait: sell the ton next year instead	$R_{t+1}$

$R_{t+1}$ above $107: waiting pays more, so keep the ton in the ground.
$R_{t+1}$ below $107: extracting pays more, so sell today.
$R_{t+1}=(1.07)R_t=\$107$: indifferent. That is Hotelling’s rule.

A ton in the ground earns no interest; its only return is a rising net price.

🔄 How the Market Enforces the Rule

If the rule fails, owners shift extraction. Extracting less in a year raises that year’s $P$ and lowers its $MC$, so its net price rises:

If	Owners	Net price today	Net price next year
$R_{t+1}>(1+r)R_t$: waiting pays	hold ore in the ground	rises ↑	falls ↓
$R_{t+1}<(1+r)R_t$: extracting pays	extract more today	falls ↓	rises ↑

Shifting stops only when $R_{t+1}=(1+r)R_t$, a no-arbitrage condition: no owner gains by moving extraction to another year.

🧲 Hotelling’s Rule in the Neodymium Model

Compute the net price on the efficient path:

Period	Quantity	Price $P$	Marginal cost $MC$	Net price $R=P-MC$
1	150 tons	$112.50	$87.50	$25
2	100 tons	$125.00	$75.00	$50

Period 2 is ten years later, so apply the annual rule ten times: $R_2=(1.0725)^{10}R_1\approx2\times\$25=\$50$, matching the table.

Equivalently, $R_1=R_2/2$: both net prices have the same present value. Since $R=P_D-P_S=MNB$, this is our condition $MNB_1=PV[MNB_2]$, which Hotelling’s rule extends to every pair of dates.

Harris and Roach, printed pp. 127–131. Prices match the depletion-tax and Period 2 slides. Read the Period 1 row as forward-looking owners with no tax: withholding 50 tons raises $P_1$ to $112.50, and the $25 is their scarcity rent, so the owner arbitrage on the previous slides applies. A $25 depletion tax gives the same prices when owners do not foresee scarcity, but then the government collects the $25 and the owner’s after-tax margin on the last Period 1 ton is $0. Tax and foresight are substitutes: an owner who foresaw scarcity and also paid the tax would over-conserve (about 117 tons in Period 1). The $25 is the equilibrium user cost; $50 is the same user cost in Period 2 dollars. At any allocation, the net price equals MNB at the quantity used, because $P$ is read off demand and $MC$ off supply; only the efficient path also satisfies $R_1=R_2/2$. Subscripts 1 and 2 here are periods, not years, and the model rounds $(1.0725)^{10}=2.01$ to 2. The match also assumes the owners’ market interest rate equals the 7.25% rate used to discount Period 2; as the ‘Which r?’ slide notes, the two need not be equal.

📈 The Benchmark Net-Price Path

Net resource price rises exponentially from 100 over 20 years at a 7 percent interest rate. — Figure 13

⛏️ The Optimal Depletion Rate

The optimal depletion rate maximizes the resource’s net present value.

Higher interest rates make earlier extraction more attractive.

Lower rates give stronger incentives to conserve.

Under the benchmark assumptions, complete exhaustion over time can be economically optimal.

Discussion: What should current users leave behind?

🏗️ Using Scarcity Rent for the Future

Hotelling asks when to extract. Hartwick asks how to use scarcity rent.

Invest scarcity rent rather than consume it.

Under the model’s assumptions, reinvesting the rent can replace lost natural wealth and help sustain consumption over time.

The rule does not preserve the neodymium deposit. It seeks to preserve the economy’s capacity to support future well-being.

This requires other forms of capital to replace the value lost through depletion. The assumption is more plausible for mineral deposits than for critical ecosystems with irreplaceable functions.

🔎 Empirical Evidence on Hotelling’s Rule

Competing forces: Better technology and new discoveries can offset depletion’s upward pressure on prices, while mining lower-quality ore can raise extraction costs.
Texas oil—Hotelling under Pressure (2018): Existing-well output barely responded to price changes, but new drilling responded strongly.
Physical limits matter: Reservoir pressure limits oil flow. Their modified Hotelling model focuses on when to drill.
Laboratory evidence (2018): With larger stocks, participants extracted too much early relative to the Hotelling benchmark and paid less attention to future scarcity.
Takeaway: Extraction constraints and how soon exhaustion matters help explain owners’ choices. Price trends alone are an incomplete test.

For the competing forces, see Harris and Roach, printed pp. 132–135. Technology can reduce extraction costs, and discoveries can expand recoverable reserves. Depleting easier deposits can raise the cost of obtaining another unit from the remaining ore.

Anderson, S. T., Kellogg, R., and Salant, S. W. (2018). “Hotelling under Pressure.” Journal of Political Economy, 126(3), 984–1026. Texas data for 1990–2007 show that existing-well production was almost unresponsive to oil-price changes, while drilling responded strongly. Low-productivity wells did shut down during the late-1990s price collapse. Reservoir pressure declines with extraction, limiting the flow from existing wells. The modified rule compares the present value of lifetime drilling revenues net of drilling costs across drilling dates. This supports a Hotelling-style model adapted to oil production, not a claim that observed $P-MC$ necessarily grew at the interest rate. The pressure mechanism does not apply to mined neodymium. Author-hosted manuscript.

van Veldhuizen, R., and Sonnemans, J. (2018). “Nonrenewable Resources, Strategic Behavior and the Hotelling Rule: An Experiment.” The Journal of Industrial Economics, 66(2), 481–516. In a controlled experiment with two resource sellers, larger stocks reduced attention to dynamic optimization and shifted extraction toward the present relative to a Hotelling benchmark allowing for market power. This offers a connection to p41: nearer exhaustion can make the future value of the stock more salient. It is laboratory evidence, not proof that real firms will allocate efficiently whenever exhaustion is near. University of Amsterdam record; working paper. The published article has a corrigendum; the university’s current abstract retains the large-stock finding.

Another useful field example is Livernois, J., Thille, H., and Zhang, X. (2006). “A Test of the Hotelling Rule Using Old-Growth Timber Data.” Canadian Journal of Economics, 39(1), 163–186. Old-growth timber is effectively nonrenewable over the relevant horizon. Auction bids for standing timber provide a directly observed scarcity-rent measure. Several specifications did not reject a modified Hotelling rule incorporating replanting and western U.S. timber institutions. This is qualified consistency, not proof, and does not make all timber nonrenewable.

🤝 Intertemporal Fairness

⚖️ Defining Intertemporal Fairness

Efficiency is mainly about eliminating waste. Fairness asks what legacy earlier generations should leave to later ones.

Future generations cannot speak for themselves, let alone bargain with the people alive today.

John Rawls argued that people should choose society’s rules without knowing whether they will end up rich or poor, powerful or disadvantaged. This veil of ignorance encourages people to choose rules that are fair to everyone.

Applied across time, people who do not know when they will be born would avoid excessive conservation, in case they are born early and must sacrifice, and excessive exploitation, in case they are born late and inherit little.

🌱 The Sustainability Criterion

One rule that could emerge from behind the veil is the sustainability criterion:

“At a minimum, future generations should be left no worse off than current generations.”

Earlier generations may use resources, even depletable ones, as long as later generations’ well-being remains at least as high as that of earlier generations.

Making later generations poorer so that earlier ones can be richer fails the test.

Question: Does the efficient neodymium allocation satisfy this criterion?

❓ Are Efficient Allocations Fair?

Period $t$’s net benefit, $NB_t$, is the trapezoid under its MNB curve. Fairness compares each period’s own well-being, so there is no discounting:

\[ NB(Q)=\frac{Q\,\times(\,100+MNB(Q)\,)}{2}=100Q-0.25Q^2. \]

Allocation	$Q_1$	$Q_2$	$NB_1$	$NB_2$
Equal split	125	125	$8,593.75	$8,593.75
Efficient, no sharing	150	100	$9,375.00	$7,500.00

Without sharing, Period 2 gets $7,500 while Period 1 gets $9,375. The efficient allocation without sharing violates the sustainability criterion.

🛢️ The Alaska Permanent Fund

Trans-Alaska Pipeline.

Oil income depletes one of Alaska’s main natural assets.
In 1976, voters amended the constitution to share oil rents with future generations.
At least 25% of mineral royalties go into the fund (50% for leases after 1979), and the principal must stay invested.

Earnings pay each eligible resident an annual dividend; the rest guards against inflation.
Dec. 2022: fund value $74.46 billion; 2022 payment $3,284 per resident, incl. a one-time $662 energy relief.

🔍 Does the Fund Achieve Full Sustainability?

The fund shares part of Alaska’s oil wealth with future generations, but it falls short of full sustainability.

The principal is not locked: a majority of current voters could approve spending it. It has been debated but not done.
Only part is saved: 25% to 50% of royalty revenue. If net oil revenue reflects scarcity rent, full sustainability would require investing 100% of it.
The current generation gets both: its share of fund income and the rest of current oil proceeds.

Discussion: What share of resource rent should a state save for future residents? Why?

🌳 Applying the Sustainability Criterion

🧭 Making the Criterion Operational

Checking whether future well-being will fall requires knowing future resource allocations and future generations’ preferences. That is a tall order.

Recall the Hartwick rule: if all scarcity rent from extraction is invested in capital, constant consumption can be maintained and the value of the total capital stock does not decline.

This reinterpretation yields two practical insights:

An annual test: a declining value of total capital signals an unsustainable path, with no forecast of future allocations or preferences needed.
A sharing rule: keeping the value of total capital from declining requires investing all scarcity rent.

💰 An Inheritance Analogy

Three paths start from a 10,000 dollar principal earning 10 percent interest. Spending 900 dollars a year makes the principal grow to about 15,700 dollars after 20 years. Spending 1,000 dollars a year keeps it constant at 10,000 dollars. Spending 1,500 dollars a year draws it down until the account is empty in year 12. — Figure 15

A $10,000 inheritance earns 10% real interest. Spending $1,000 or less a year is sustainable; spending more is not. Test: Is the principal declining?

🌳 Keep the Principal Intact

The current generation inherits an endowment of natural capital (environmental and natural resources) and physical capital (buildings, equipment, schools, and roads).

Sustainable use keeps the value of this combined endowment intact and lives off the flow of services it provides. This is weak sustainability: natural capital may fall if physical or financial capital rises enough to offset it.

Depleting trees or oil is not the problem by itself; consuming their value without replacing it is.

This works only if physical capital can substitute for natural capital. Air-conditioned domed cities would be a poor substitute for breathable air.

🏝️ Nauru: Weak Sustainability in the Extreme

Pinnacles left by phosphate mining, Nauru.

A small Pacific island with some of the highest-grade phosphate ever discovered.
A century of mining turned phosphate into financial capital: a trust fund once believed to exceed $1 billion.

Mining destroyed most of the island’s ecosystems, so Nauru could produce little for itself. By the late 1990s, it relied on imports paid for with phosphate income.
Not replicable globally: “every import must be exported by someone.”

Weak sustainability may be necessary, but it is not always sufficient.

Tietenberg and Lewis, Example 5.2, printed pp. 124–125. Nauru lies about 3,000 kilometers northeast of Australia, and phosphate is a prime ingredient in fertilizer. Mining was carried out first under colonial administrations and then, after independence, by Nauruans themselves. The example draws on Gowdy and McDaniel (1999), “The Physical Destruction of Nauru: An Example of Weak Sustainability,” Land Economics, 75(2), 333–338. Postscript: the Nauru Phosphate Royalties Trust was later largely lost through poor investments and mismanagement, so even the financial capital meant to replace the phosphate was not maintained (Development Policy Centre, https://devpolicy.org/nauru-riches-to-rags-to-riches-20210412/). Image: Sean Kelleher, “Pinnacles after secondary mining,” 2013, CC BY-SA 2.0, https://commons.wikimedia.org/wiki/File:Pinnacles_after_secondary_mining_(15227476278).jpg.

🧭 Three Definitions of Sustainability

Definition	What must not decline	Substitution view
Weak	Value of total capital: natural plus physical	Physical capital can replace natural capital
Strong	Value of natural capital	Little or no substitution is possible
Environmental	Physical flows of key individual resources	Maintaining an aggregate value is not enough

Fishery: under environmental sustainability, catch should not exceed the growth of the fish population.
Wetland: its specific ecological functions should be preserved.

🎯 Sustainability and Policy

🧩 Efficiency and Sustainability Are Different Tests

To be useful for policy, the two tests must differ without being in conflict.

Efficient

Inefficient

Sustainable

Efficient and sustainable
The policy target

Sustainable but inefficient
Net benefits are wasted

Unsustainable

Efficient but unsustainable
Later generations end up worse off

Inefficient and unsustainable
Room for win–win reform

Market allocations can fall into any of the four cells.

🎯 Implications for Environmental Policy

Treat sustainability as an overriding constraint on social decisions.

By itself, the sustainability criterion cannot choose among the infinite number of sustainable allocations.

Efficiency fills that gap: among the sustainable allocations, pick the one with the greatest dynamic or static efficiency.

Maximize net benefits subject to the sustainability constraint.

🤝 Win–Win Changes

Inefficiency is a common cause of unsustainable allocations.

Fixing the inefficiency can restore sustainability or bring the economy much closer to it.

Some reforms remove wasteful resource use, increasing net benefits while helping preserve resources for future generations. If the gains exceed the losses, those who benefit can use part of their gains to compensate those who would otherwise lose.

A win–win improvement is possible when all affected parties can be made better off. Whether this happens depends on how the gains are shared.

Discussion: Do markets and political institutions usually deliver outcomes that are both efficient and sustainable?